An option pricing model is developed based on a generalized autoregressive conditional heteroskedastic (GARCH) asset return process with stable Paretian innovations. Our approach is based on the locally risk-neutral valuation relationship. Methods for maximum likelihood estimation of GARCH-stable processes are presented as well as empirical results for the DAX index. Finally, the results of Monte Carlo simulations evaluating prices of European call options, implied volatility, delta hedging parameters, and value at risk are presented.
- GARCH-stable processes
- Locally risk-neutral valuation
- Option pricing
- Stable distributions